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This Demonstration shows the oscillations of a system composed of two identical springs with force constant

attached to a disk of radius

and mass

that rolls without sliding on a plane inclined at angle

. The resultant amplitude is

Using Newton's second law, it is possible to establish the equilibrium point

, where

is the length of the incline,

is the acceleration due to gravity, and

is a parameter that determines the rotation of the wheel. By energy conservation, one can find the angular frequency:

. From this, the equation of motion for the

coordinate, measured along the surface, is found to be

. The parameters

, and

all appear in the result.

(Universidad del Valle sede Buga. Guadalajara de Buga, Colombia, Sudamérica)

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Oscillations of a Mass-Spring System on an Inclined Plane